Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1198.47078
Zhai, Cheng-Bo; Yang, Chen; Zhang, Xiao-Qin
Positive solutions for nonlinear operator equations and several classes of applications. (English)
[J] Math. Z. 266, No. 1, 43-63 (2010). ISSN 0025-5874; ISSN 1432-1823/e

The authors study a class of nonlinear operator equations $x = Ax + x _{0}$ on ordered Banach spaces, where $A$ is a monotone generalized concave operator. Employing the properties of cones and monotone iterative technique, they prove existence and uniqueness of solutions for such equations without requiring existence of upper-lower solutions and compactness and continuity conditions. Applications are proposed to first-order initial value problems and two-point boundary value problems with nonlinear term which is monotone with respect to its second argument, as well as to nonlinear systems of equations and to nonlinear matrix equations.
[Dian K. Palagachev (Bari)]

MSC 2000:: *47J05 Equations involving nonlinear operators (general)
47N20 Appl. of operator theory to differential and integral equations
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H07 Positive operators on ordered topological linear spaces
34B18 Positive solutions of nonlinear boundary value problems
35F25 Initial value problems for first order nonlinear PDE
15A30 Algebraic systems of matrices

Keywords: positive solution; nonlinear operator equation; normal cone; initial value problem; boundary value problem; nonlinear algebra systems

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]